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Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and...

Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows:

Department Product 1 Product 2 Product 3
A 1.70 3.20 2.20
B 2.40 1.40 2.90
C 0.45 0.45 0.45

During the next production period, the labor-hours available are 490 in department A, 390 in department B, and 90 in department C. The profit contributions per unit are $29 for product 1, $32 for product 2, and $34 for product 3. Use a software package LINGO.

  1. Formulate a linear programming model for maximizing total profit contribution. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) If constant is “1”, it must be entered in the box.

    Let Pi = units of product i produced
    Max ______P1 + ______P2 + ______P3
    s.t.
    ______P1 + ______P2 + ______P3 ≤ ______
    ______P1 + ______P2 + ______P3 ≤ ______
    ______P1 + ______P2 + ______P3 ≤ ______
    P1, P2, P3 ≥ 0
  2. Solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contribution?

    P1 = ______
    P2 = ______
    P3 = ______

    Profit = $  ______
  3. After evaluating the solution obtained in part (b), one of the production supervisors noted that production setup costs had not been taken into account. She noted that setup costs are $440 for product 1, $590 for product 2, and $640 for product 3. If the solution developed in part (b) is to be used, what is the total profit contribution after taking into account the setup costs?

    Profit = $  ______
  4. Management realized that the optimal product mix, taking setup costs into account, might be different from the one recommended in part (b). Formulate a mixed-integer linear program that takes setup costs into account. Management also stated that we should not consider making more than 195 units of product 1, 170 units of product 2, or 160 units of product 3. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) If constant is “1”, it must be entered in the box. Enter “0” if your answer is zero.

    Here introduce a 0-1 variable yi that is one if any quantity of product i is produced and zero otherwise.
    Max ______P1 + ______P2 + ______P3 + ______y1 + ______y2 + ______y3
    s.t.
    ______P1 + ______P2 + ______P3 ≤ ______
    ______P1 + ______P2 + ______P3 ≤ ______
    ______P1 + ______P2 + ______P3 ≤ ______
    ______P1 + ______y1 ≤ ______
    ______P2 + ______y2 ≤ ______
    ______P3 + ______y3 ≤ ______
    P1, P2, P3 ≥ 0; y1, y2, y3 = 0, 1
  5. Solve the mixed-integer linear program formulated in part (d). How much of each product should be produced, and what is the projected total profit contribution? Compare this profit contribution to that obtained in part (c). Enter “0” if your answer is zero.

    P1 = ______
    P2 = ______
    P3 = ______

    Profit = $  ______

    The profit is increased by $ ______.

Please fill out all the blanks! Thank you!!

Solutions

Expert Solution

milcah answered 3 hours ago
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